Related papers: On K\"ahler Ricci shrinker surfaces

By establishing two general quadratic inequalities, we obtain some inequalities related to Ricci curvatures for Lagrangian submanifolds of K$\ddot{\mathrm{a}}$hler QCH-manifolds, which generalize some results for Lagrangian submanifolds of…

We consider the K\"ahler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the K\"ahler-Ricci flow, then the diameter is uniformly bounded. As a corollary we show that…

We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…

We establish the existence of K\"ahler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously complete, and its normalized version converge to the complete…

We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by F. Marques and A. Neves. We prove this by analyzing…

A projectability result is proved for surfaces of prescribed mean curvature (shortly called $H$-surfaces) spanned in a partially free boundary configuration. Hereby, the $H$-surface is allowed to meet the support surface along its free…

This note proves orbifold versions of Kobayashi's theorem. The main result asserts that a compact K\"ahler orbifold with non-negative Ricci curvature, along with certain conditions regarding singularities, is simply connected.

In this paper, we proved a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

In this note, we prove a 2-systolic inequality on compact positive scalar curvature K\"ahler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surface. According to the classification of positive scalar…

In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2\pi$. In this case, convergence results are obtained if the Euler number is nonpositive.

In this paper we prove the compactness result for compact K\"ahler Ricci gradient shrinking solitons. If $(M_i,g_i)$ is a sequence of K\"ahler Ricci solitons of real dimension $n \ge 4$, whose curvatures have uniformly bounded $L^{n/2}$…

In this work, we obtain a existence criteria for the longtime K\"ahler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of K\"ahler Einstein metric to the case with possibly unbounded…

We record two remarks. First, for a compact K\"ahler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact K\"ahler…

In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)\lambda$ must have vanished second fundamental form and vanished normal Ricci…

We give a complete equisingular deformation classification of simple spatial quartic surfaces which are in fact $K3$-surfaces.

We prove that any singular K\"ahler--Ricci shrinker $X$ arising as a noncollapsed limit of K\"ahler--Ricci flows admits a natural structure of a locally algebraic complex-analytic variety with log terminal singularities. We then derive…

In this short note, we use classic computations for K\"ahler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.

In this work, we investigate compact K\"ahler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature…

In this paper, we consider orthogonal Ricci curvature $Ric^{\perp}$ for K\"ahler manifolds, which is a curvature condition closely related to Ricci curvature and holomorphic sectional curvature. We prove comparison theorems and a vanishing…

We conjecture that any scalar-flat K\"ahler surface in which the Weyl tensor acting on 2-forms annihilates the Ricci form must be either Ricci-flat or locally isometric to a Riemannian product of two real surfaces with mutually opposite…